Problem: Simplify the following expression: $ q = \dfrac{n - 9}{-9n + 4} - \dfrac{-1}{6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{n - 9}{-9n + 4} \times \dfrac{6}{6} = \dfrac{6n - 54}{-54n + 24} $ Multiply the second expression by $\dfrac{-9n + 4}{-9n + 4}$ $ \dfrac{-1}{6} \times \dfrac{-9n + 4}{-9n + 4} = \dfrac{9n - 4}{-54n + 24} $ Therefore $ q = \dfrac{6n - 54}{-54n + 24} - \dfrac{9n - 4}{-54n + 24} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{6n - 54 - (9n - 4) }{-54n + 24} $ Distribute the negative sign: $q = \dfrac{6n - 54 - 9n + 4}{-54n + 24}$ $q = \dfrac{-3n - 50}{-54n + 24}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{3n + 50}{54n - 24}$